The revenge of the Patterson methods. II. Substructure applications

The single-atom R1: a new optimization method to solve crystal structures

A crystal structure with N atoms in its unit cell can be solved starting from a model with atoms 1 to j - 1 being located. To locate the next atom j, the method uses a modified definition of the traditional R1 factor where its dependencies on the locations of atoms j + 1 to N are removed. This modified R1 is called the single-atom R1 (sR1), because the locations of atoms 1 to j - 1 in sR1 are the known parameters, and only the location of atom j is unknown. Finding the correct position of atom j translates thus into the optimization of the sR1 function, with respect to its fractional coordinates, xj, yj, zj. Using experimental data, it has been verified that an sR1 has a hole near each missing atom. Further, it has been verified that an algorithm based on sR1, hereby called the sR1 method, can solve crystal structures (with up to 156 non-hydrogen atoms in the unit cell). The strategy to carry out this calculation has also been optimized. The main feature of the sR1 method is that, starting from a single arbitrarily positioned atom, the structure is gradually revealed. With the user's help to delete poorly determined parts of the structure, the sR1 method can build the model to a high final quality. Thus, sR1 is a viable and useful tool for solving crystal structures.

Synergy among phase-refinement techniques in macromolecular crystallography

Ab initio and non-ab initio phasing methods are often unable to provide phases of sufficient quality to allow the molecular interpretation of the resulting electron-density maps. Phase extension and refinement is therefore a necessary step: its success or failure can make the difference between solution and nonsolution of the crystal structure. Today phase refinement is trusted to electron-density modification (EDM) techniques, and in practice to dual-space methods which try, via suitable constraints in direct and in reciprocal space, to generate higher quality electron-density maps. The most popular EDM approaches, denoted here as mainstream methods, are usually part of packages which assist crystallographers in all of the structure-solution steps from initial phasing to the point where the molecular model perfectly fits the known features of protein chemistry. Other phase-refinement approaches that are based on different sources of information, denoted here as out-of-mainstream methods, are not frequently employed. This paper aims to show that mainstream and out-of-mainstream methods may be combined and may lead to dramatic advances in the present state of the art. The statement is confirmed by experimental tests using molecular-replacement, SAD-MAD and ab initio techniques.

VLD algorithm and hybrid Fourier syntheses

The VLD (vive la difference) phasing algorithm combines the model electron density with the difference electron densityviareciprocal space relationships to obtain new phase values and drive them to the correct values. The process is iterative and has been applied to small and medium-size structures and to proteins. Hybrid Fourier syntheses show properties that are intermediate between those of the observed synthesis (whose peaks should correspond to the most probable atomic positions) and those of the difference synthesis (whose positive and negative peaks should correspond to missed atomic positions and to false atoms of the model, respectively). Thanks to these properties some hybrid syntheses can be used in the phase extension and refinement step, to reduce the model bias and more rapidly move to the target structure. They have been recently revisitedviathe method of joint probability distribution functions [Burla, Carrozzini, Cascarano, Giacovazzo & Polidori (2011).Acta. Cryst. A67, 447–455]. The results suggested that VLD could be usefully combined, forab initiophasing, with the hybrid rather than with the difference Fourier synthesis. This paper explores the feasibility of such a combination and shows that the original VLD algorithm is only one of several variants, all with relevant phasing capacity. The study explores the role of several parameters in order to design a standard procedure with optimized phasing power.